32.9.19 problem Exercise 22, problem 19, page 240

Internal problem ID [5993]
Book : Ordinary Differential Equations, By Tenenbaum and Pollard. Dover, NY 1963
Section : Chapter 4. Higher order linear differential equations. Lesson 22. Variation of Parameters
Problem number : Exercise 22, problem 19, page 240
Date solved : Monday, January 27, 2025 at 01:30:31 PM
CAS classification : [[_2nd_order, _exact, _linear, _nonhomogeneous]]

\begin{align*} x^{2} y^{\prime \prime }+x y^{\prime }-y&=x^{2} {\mathrm e}^{-x} \end{align*}

✓ Solution by Maple

Time used: 0.003 (sec). Leaf size: 25

dsolve(x^2*diff(y(x),x$2)+x*diff(y(x),x)-y(x)=x^2*exp(-x),y(x), singsol=all)
 

\[ y \left (x \right ) = \frac {c_{2} x^{2}+x \,{\mathrm e}^{-x}+{\mathrm e}^{-x}+c_{1}}{x} \]

✓ Solution by Mathematica

Time used: 0.026 (sec). Leaf size: 27

DSolve[x^2*D[y[x],{x,2}]+x*D[y[x],x]-y[x]==x^2*Exp[-x],y[x],x,IncludeSingularSolutions -> True]
 

\[ y(x)\to \frac {c_2 x^2+e^{-x} (x+1)+c_1}{x} \]